The product rule of exponents states that when you multiply two expressions with the same base, you add the exponents. In other words, \( a^m \times a^n = a^{m+n} \).
Let's analyze each option:
A. \( 10^8 \cdot 10^8 \)
- This can be simplified using the product rule: \( 10^{8+8} = 10^{16} \).
B. \( 32^7 \)
- This expression does not involve the multiplication of two expressions with the same base, so it does not apply the product rule.
C. \( (5^2)^9 \)
- This uses the power of a power rule, which states that \( (a^m)^n = a^{m \cdot n} \). It is not a product of two expressions, so it does not apply the product rule.
D. \( 6^2 \cdot 7^3 \)
- This involves multiplying bases that are not the same, so it does not use the product rule.
The only option that is developed to use the product rule of exponents is A. \( 10^8 \cdot 10^8 \).
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